Computer Algebra Recipes: An Advanced Guide to Scientific Modeling

Modern computer algebra systems are revolutionizing the teaching and learning of mathematically intensive subjects in science and engineering, enabling students to explore increasingly complex and computationally intensive models that provide analytic solutions, animated numerical solutions, and complex two- and three-dimensional graphic displays. This self-contained text benefits from a spiral structure that regularly revisits the general topics of graphics, symbolic computation, and numerical simulation with increasing intricacy at each turn. The text is built around a large number of computer algebra worksheets or "recipes" that have been designed using MAPLE to provide tools for problem solving and to stimulate critical thinking. No prior knowledge of MAPLE is assumed. All relevant commands are introduced on a need-to-know basis and are indexed for easy reference. Each recipe is associated with a scientific model or method and an interesting or amusing story designed to both entertain and enhance concept comprehension and retention. All recipes are included on the CD-ROM enclosed with the book. Aimed at third- and fourth-year undergraduates in science and engineering, the text contains numerous examples in disciplines that will challenge students progressing in mathematics, physics, engineering, game theory, and physical chemistry. Computer Algebra Recipes: An Advanced Guide to Mathematical Modeling can serve as an effective computational science text, with a set of problems following each section of recipes to enable readers to apply and confirm their understanding. The book may also be used as a reference, for self-study, or as the basis of an on-line course.

Table of Contents:
The Appetizers.- Phase-Plane Portraits.- Phase-Plane Analysis.- The Entrees.- Linear ODE Models.- Nonlinear ODE Models.- Linear PDE Models. Part 1.- Linear PDE Models. Part 2.- The Desserts.- The Hunt for Solitons.- Nonlinear Diagnostic Tools.

Review :
"This book is written in the same spirit as the earlier text [Computer algebra recipes for mathematical physics. In accordance with the title of the book, the three chapters of the book are named as follows: I. The appetizers; II. The entrees; III. The deserts. Each chapter is divided into several dozens of subsections, patterned in the same way: a cover story about a modelling problem, some mathematical background, Maple solution of the problem with graphics, a set of problems. No prior knowledge of Maple is required from the reader: the authors suggest that new users of Maple read the book in natural order while experiences users may skip some parts and go directly to the topic of their interest. The cover stories are chosen from most diverse subjects that well describe the universal role of scientific modelling. A central theme is the use of systems of ordinary differential equations with many variations. For instance the love affair between Romeo and Juliet is analyzed in this way." (Matti Vuorinen, Zentralblatt MATH)